New theoretical modeling for predicting yarn angle on OE yarn influenced by fibre movement on torus coordinate based on classical mechanics approach

In this study, fibre movement inside yarn has been analyzed using geodesic equation on torus coordinate. By understanding the trace of fibre movement inside the open-end (OE) yarn, the relation of twist and angle of twist can be established well. In this new model, the equation of fibre movement has been found and the relationship of angle of twist to diameter of yarn is well formulated.